Prépublication AOC numéro 03-13

Some Variational Characterizations of Beer's Affine Convergence.
GEOFFROY, Michel H. - Laboratoire A.O.C., Université des Antilles et de la Guyane, Pointe-à-Pitre, F-97159 cedex

In 1989, Beer defined the so called affine topology on G(X) (the space of proper lower semicontinuous convex functions on X) with respect to which the value functional enjoys some nice properties. He also gave a characterization of the corresponding concept of convergence on G(X) when X is a reflexive Banach space. In this paper we provide several characterizations of Beer's affine convergence on G(X) when X is a general Banach space. The first one involves gap functionals whereas the main result characterizes the affine convergence in terms of convergence of infima, subdifferentials and slopes.